识别热带线性簇的多项式复杂性

热带隐式化与混合纤维多面体

Tropical Implicitization and Mixed Fiber Polytopes

软件TrIm提供了Tevelev和作者开发的热带隐含化和热带消除的实现。给定具有通用系数的多项式映射，TrIm计算图像的热带变化。当图像是超曲面时，输出是定义多项式的牛顿多面体。因此，TrIm可以用于计算混合纤维多面体，包括二级多面体。

Parallel Computation of tropical varieties, their positive part, and tropical Grassmannians

In this article, we present a massively parallel framework for computing tropicalizations of algebraic varieties which can make use of finite symmetries. We compute the tropical Grassmannian TGr$_0(3,8)$, and show that it refines the $15$-dimensional skeleton of the Dressian Dr$(3,8)$ with the exception of $23$ special cones for which we construct explicit obstructions to the realizability of their tropical linear spaces. Moreover, we propose algorithms for identifying maximal-dimensional tropical cones which belong to the positive tropicalization. These algorithms exploit symmetries of the tr…